Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This paper shows that there are symplectic four-manifolds M with the following property: a single isotopy class of smooth embedded two-spheres in M contains infinitely many Lagrangian submanifolds, no two of which are isotopic as Lagrangian submanifolds. The examples are constructed using a special class of symplectic automorphisms ("generalized Dehn twists"). The proof uses Floer homology. 
Revised version: one footnote removed, one reference added

Lagrangian two-spheres can be symplectically knotted

In [10], we construct an exotic monotone Lagrangian torus in CP 2 (not Hamiltonian isotopic to the known Clifford and Chekanov tori) using techniques motivated by mirror symmetry. We named it T(1,4,25) because, when following a degeneration of CP 2 to the orbifold CP(1,4,25), it degenerates to the central fiber of the moment map for the standard torus action on CP(1,4,25). Related to each degeneration from CP 2 to CP(a 2 ,b 2 ,c 2 ), for (a,b,c) a Markov triple - see (1.1) - there is a monotone Lagrangian torus, which we call T(a 2 ,b 2 ,c 2 ). We conjectured that no two of them are Hamiltonian isotopic to each other. Here we employ techniques from symplectic field theory to prove that the above conjecture is true.

Infinitely many exotic monotone Lagrangian tori in ℂℙ2

We prove that the wrapped Fukaya category of any $2n$-dimensional Weinstein manifold (or, more generally, Weinstein sector) $W$ is generated by the unstable manifolds of the index $n$ critical points of its Liouville vector field. Our proof is geometric in nature, relying on a surgery formula for Floer homology and the fairly simple observation that Floer homology vanishes for Lagrangian submanifolds that can be disjoined from the isotropic skeleton of the Weinstein manifold. Note that we do not need any additional assumptions on this skeleton. By applying our generation result to the diagonal in the product $W \times W$, we obtain as a corollary that the open-closed map from the Hochschild homology of the wrapped Fukaya category of $W$ to its symplectic cohomology is an isomorphism, proving a conjecture of Seidel. We work mainly in the ``linear setup'' for the wrapped Fukaya category, but we also sketch the minor modifications which we need to extend the proofs to the ``quadratic setup'' and to the ``localisation setup''. This is necessary for dealing with Weinstein sectors and for the applications.

Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors

Numerical simulation of seawater intrusion to coastal aquifers and brine water/freshwater interaction in south coast of Laizhou Bay, China

University of Minnesota Ph.D. dissertation. July 2012. Major: Mathematics. Advisor: Tian-Jun Li. 1 computer file (PDF); iii, 61 pages.

/pdf/lagrangian-spheres-symplectic-surfaces-and-the-symplectic-5bp2jtg1bc.pdf

Lagrangian spheres, symplectic surfaces and the symplectic mapping class group

Given a Lagrangian sphere in a symplectic 4-manifold $(M, \omega)$ with $b^+=1$, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension $\kappa$ of $(M, \omega)$ is $-\infty$, this minimal intersection property turns out to be very powerful for both the uniqueness and existence problems of Lagrangian spheres. On the uniqueness side, for a symplectic rational manifold and any class which is not characteristic and ternary, we show that homologous Lagrangian spheres are smoothly isotopic, and when the Euler number is less than 8, we generalize Hind and Evans' Hamiltonian uniqueness in the monotone case. On the existence side, when $\kappa=-\infty$, we give a characterization of classes represented by Lagrangian spheres, which enables us to describe the non-Torelli part of the symplectic mapping class group.

/pdf/lagrangian-spheres-symplectic-surfaces-and-the-symplectic-3xu57v1h5u.pdf

This paper introduces a new Lagrangian surgery construction that generalizes Lalonde–Sikorav and Polterovich’s well-known construction, and combines this with Biran and Cornea’s Lagrangian cobordism formalism. With these techniques, we build a framework which both recovers several known long exact sequences (Seidel’s exact sequence, including the fixed point version and Wehrheim and Woodward’s family version) in symplectic geometry in a uniform way, and yields a partial answer to a long-term open conjecture due to Huybrechts and Thomas; this also involved a new observation which relates projective twists with surgeries.

Dehn twists exact sequences through Lagrangian cobordism

In this paper, we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, $$S^{2}$$
 or $$\mathbb{RP }^{2}$$
 , in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction, this is a natural extension of McDuff’s connectedness of ball packings in other settings and this result has applications to several different questions: smooth knotting and unknottedness results for spherical Lagrangians, the transitivity of the action of the symplectic Torelli group, classifying Lagrangian isotopy classes in the presence of knotting, and detecting Floer-theoretically essential Lagrangian tori in the del Pezzo surfaces.

Spherical Lagrangians via ball packings and symplectic cutting

We find a non-displaceable Lagrangian torus fiber in a semi-toric system which is superheavy with respect to a certain symplectic quasi-state. The proof employs both 4-dimensional techniques and those from symplectic field theory. In particular, our result implies Lagrangian $\mathbb{R}P^{2}$
 is not a stem in $\mathbb{C}P^{2}$
 , answering a question of Entov and Polterovich.

/pdf/on-an-exotic-lagrangian-torus-in-10xx0acb0p.pdf

Weiwei Wu

Papers

Lagrangian spheres, symplectic surfaces and the symplectic mapping class group

Lagrangian spheres, symplectic surfaces and the symplectic mapping class group

Dehn twists exact sequences through Lagrangian cobordism

Spherical Lagrangians via ball packings and symplectic cutting

On an exotic Lagrangian torus in